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Conformal mappings and shape derivatives for the transmission problem with a single measurement.

Lekbir Afraites 1, Marc Dambrine 1, Djalil Kateb 1

(07/03/2006)

In the present work, we consider the inverse conductivity problem of recovering inclusion with one measurement. First, we use conformal mapping techniques for determining the location of the anomaly and estimating its size. We then get a good initial guess for quasi-Newton type method. The inverse problem is treated from the shape optimization point of view. We give a rigorous proof for the existence of the shape derivative of the state function and of shape functionals. We consider both Least Squares fitting and Kohn and Vogelius functionals. For the numerical implementation, we use a parametrization of shapes coupled with a boundary element method. Several numerical exemples indicate the superiority of the Kohn and Vogelius functional over Least Squares fitting.

1 :	Laboratoire de Mathématiques Appliquées de Compiègne - EA2222 (LMAC)
	Université de Technologie de Compiègne

Domaine

:

Mathématiques/Optimisation et contrôle

Mots Clés : inverse conductivity problem – shape optimization – shape derivatives – conformal mappings – boundary element methods.

hal-00020177, version 1

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Contributeur : Marc Dambrine <>

Soumis le : Mardi 7 Mars 2006, 12:53:27

Dernière modification le : Mardi 7 Mars 2006, 13:51:35